Complete the Prime Number: What Digit Fills in the Blank for _7?

To solve the problem, we must identify which digit replaces the placeholder in $\square7$ to make a prime number. The choices provided are $1, 2, 5,$ and $7$.

Let's test each choice:

• Substitute $1$: The number becomes $17$. Check if it's prime.

• Substitute $2$: The number becomes $27$. Check if it's prime.

• Substitute $5$: The number becomes $57$. Check if it's prime.

• Substitute $7$: The number becomes $77$. Check if it's prime.

Let's evaluate each result:

• $17$: $17$ is not divisible by any number, hence it is prime.

• $27$: Not prime (divisible by $3$).

• $57$: Not prime (divisible by $3$).

• $77$: Not prime (divisible by $7$).

Therefore, the only prime number formed is $17$.

Thus, the correct digit that makes the number $\square7$ a prime number is $1$, and the complete number is $17$.